Having a story puplished as a serial?

If you have a short story far too long for publication by most magazines is it worth asking the editor to think about publishing it as a serial?

And if you have a short story set into a few small parts, is it worth submitting each part to that magazine as a serial over a few issues, or is this too much of a risk.

I ask this, as I am writing a short story now that I have set into three sections of around 1,500 - 2,000 words in length and if I wish to attempt to publish it in the future, is this something worth considering as a lot of the magazines I have came across only accept stories up to and around 2,000 words in length where this is around 6,000.

As far as short fiction goes, I've sold stories that range from 2300 up to 9100 words in length. If your story is going to be 5-6000 words, in most genres, many markets accept 5000 word stories, and a few up to 10,000. Not many publish serials regularly, but there are some.